Gaussian Process Regression Research Articles

Exploring the Effects of Topography on Leaf Area Index Retrieved from Remote Sensing Data at Various Spatial Scales over Rugged Terrains

Topography significantly affects remotely sensed reflectance data and subsequently impacts the retrieval of the leaf area index (LAI) from surface reflectance data over rugged terrains. However, most LAI inversion algorithms ignore the influence of terrain. This paper quantitatively analyzes the topographic effects on LAI values retrieved from remote sensing data at various spatial scales (30, 90, 270, 540, 1080, and 5400 m) over rugged terrains. The PRO4SAILT (PROSPECT + 4SAILT) model and the Proy algorithm were used to simulate multiscale surface reflectance for different LAI values over rugged terrains. Based on Gaussian process regression (GPR), an LAI inversion algorithm that ignores terrain effects was first developed. The simulated multiscale reflectance data were subsequently input into the inversion algorithm to retrieve LAI values. Finally, the retrieved LAI values were compared with the corresponding reference LAI values. The results demonstrate that the finer the spatial resolution is, the more significant the topographic effects on the retrieved LAI values are. When the reference LAI is five, as the spatial resolution increases from 5400 m to 30 m, the mean percentage error (MPE) of the retrieved LAI increases from 10.46% to 13.72%, and the root mean square error (RMSE) increases from 0.5376 to 1.005. Regardless of the spatial resolution, the error in the retrieved LAI values increases with an increasing terrain slope. When the reference LAI is five and the spatial resolution is 30 m, the MPE at a slope of 15°–30° is close to 5%, and the RMSE is close to 0.3. The MPE at a slope of 30°–45° is close to 20%, and the RMSE is close to one. In addition, the accuracy of the retrieved LAI values is closely related to the sky view factor (SVF). In general, the larger the SVF is, the smaller the error in the retrieved LAI values. In addition, the conversion relationships between the retrieved LAI values using the algorithm that ignores terrain effects and the true LAI values are provided in this study.

Data-Based In-Cylinder Pressure Model with Cyclic Variations for Combustion Control: An RCCI Engine Application

Cylinder-pressure-based control is a key enabler for advanced pre-mixed combustion concepts. In addition to guaranteeing robust and safe operation, it allows for cylinder pressure and heat release shaping. This requires fast control-oriented combustion models. Over the years, mean-value models have been proposed that can predict combustion metrics (e.g., gross indicated mean effective pressure (IMEPg), or the crank angle where 50% of the total heat is released (CA50)) or models that predict the full in-cylinder pressure. However, these models are not able to capture cycle-to-cycle variations. The inclusion of the cycle-to-cycle variations is important in the control design for combustion concepts, like reactivity-controlled compression ignition, that can suffer from large cycle-to-cycle variations. In this study, the in-cylinder pressure and cycle-to-cycle variations are modelled using a data-based approach. The in-cylinder conditions and fuel settings are the inputs to the model. The model combines principal component decomposition and Gaussian process regression. A detailed study is performed on the effects of the different hyperparameters and kernel choices. The approach is applicable to any combustion concept, but is most valuable for advance combustion concepts with large cycle-to-cycle variation. The potential of the proposed approach is successfully demonstrated for a reactivity-controlled compression ignition engine running on diesel and E85. The average prediction error of the mean in-cylinder pressure over a complete combustion cycle is 0.051 bar and of the corresponding mean cycle-to-cycle variation is 0.24 bar2. This principal-component-decomposition-based approach is an important step towards in-cylinder pressure shaping. The use of Gaussian process regression provides important information on cycle-to-cycle variation and provides next-cycle control information on safety and performance criteria.

Combining Autoregressive Integrated Moving Average Model and Gaussian Process Regression to Improve Stock Price Forecast

Stock market performance is one key indicator of the economic condition of a country, and stock price forecasting is important for investments and financial risk management. However, the inherent nonlinearity and complexity in stock price movements imply that simple conventional modeling techniques are not adequate for stock price forecasting. In this paper, we present a hybrid model (ARIMA + GPRC) which combines the autoregressive integrated moving average (ARIMA) model and Gaussian process regression (GPR) with a combined covariance function (GPRC). The proposed hybrid model can account for both the linearity and nonlinearity in stock price movements. Based on daily data on three stocks listed on the Shanghai Stock Exchange (SSE), it is found that GPRC outperforms GPR with a single covariance function. Further, the proposed hybrid model is compared with the ARIMA model, artificial neural network (ANN), and GPRC model. Based on the forecasting trend and the statistical performance of the four models, the ARIMA + GPRC model is found to be the dominant model for stock price forecasting and can significantly improve forecasting performance.

Contribution to advancing aquifer geometric mapping using machine learning and deep learning techniques: a case study of the AL Haouz-Mejjate aquifer, Marrakech, Morocco

Groundwater resources in Morocco often face sustainability challenges due to increased exploitation and climate change. Specifically, the Al-Haouz-Mejjate groundwater in the Marrakesh region is faced with overexploitation and insufficient recharge. However, the complex subsurface geometries hamper hydrogeological modeling, characterization, and effective management. Reliably estimating aquifer substrate topography is critical for groundwater models but is challenged by limited direct measurements. This study develops nonlinear machine learning models to infer substrate depths by fusing sparse borehole logs with regional geospatial data. A Gaussian process regression approach provided robust holistic mapping, leveraging flexibility, and uncertainty quantification. Supplementary neural network architectures focus on isolating specific variable relationships, like surface elevation–substrate. Model accuracy exceeded 0.8 R-squared against validation boreholes. Spatial visualizations confirmed consistency across landscape transects. Elevation and piezometric data proved most predictive, though multivariate inputs were required for the lowest errors. The results highlight the power of statistical learning to extract meaningful patterns from disparate hydrological data. However, model opacity and the need for broader training datasets remain barriers. Overall, the work demonstrates advanced machine learning as a promising avenue for illuminating complex aquifer geometries essential for sustainability. Hybrid approaches that use both data-driven and physics-based methods can help solve long-standing problems with hydrogeological characterization.

Thermal and Energy Transport Prediction in Non-Newtonian Biomagnetic Hybrid Nanofluids using Gaussian Process Regression

Thermal and Energy Transport Prediction in Non-Newtonian Biomagnetic Hybrid Nanofluids using Gaussian Process Regression

Optimal Microphone Array Placement Design Using the Bayesian Optimization Method

In addition to the filter coefficients, the location of the microphone array is a crucial factor in improving the overall performance of a beamformer. The optimal microphone array placement can considerably enhance speech quality. However, the optimization problem with microphone configuration variables is non-convex and highly non-linear. Heuristic algorithms that are frequently employed take a long time and have a chance of missing the optimal microphone array placement design. We extend the Bayesian optimization method to solve the microphone array configuration design problem. The proposed Bayesian optimization method does not depend on gradient and Hessian approximations and makes use of all the information available from prior evaluations. Furthermore, Gaussian process regression and acquisition functions make up the Bayesian optimization method. The objective function is given a prior probabilistic model through Gaussian process regression, which exploits this model while integrating out uncertainty. The acquisition function is adopted to decide the next placement point based upon the incumbent optimum with the posterior distribution. Numerical experiments have demonstrated that the Bayesian optimization method could find a similar or better microphone array placement compared with the hybrid descent method and computational time is significantly reduced. Our proposed method is at least four times faster than the hybrid descent method to find the optimal microphone array configuration from the numerical results.

Multivariate Gaussian process surrogates for predicting basic structural parameters of refractory non-dilute random alloys

Refractory non-dilute random alloys consist of two or more principal refractory metals with complex interactions that modify their basic structural properties such as lattice parameters and elastic constants. Atomistic simulations (ASs) are an effective method to compute such basic structural parameters. However, accurate predictions from ASs are computationally expensive due to the size and number of atomistic structures required. To reduce the computational burden, multivariate Gaussian process regression (MVGPR) is proposed as a surrogate model that only requires computing a small number of configurations for training. The elemental atom percentage in the hyper-spherical coordinates is demonstrated to be an effective feature for surrogate modeling. An additive approximation of the full MVGPR model is also proposed to further reduce computations. To improve surrogate accuracy, active learning is used to select a small number of alloys to simulate. Numerical studies based on AS data show the accuracy of the surrogate methodology and the additive approximation, as well as the effectiveness and robustness of the active learning for selecting new alloy designs to simulate.

Underluminous 1991bg-like Type Ia supernovae are standardizable candles

Abstract It is widely accepted that the width-luminosity relation used to standardize normal Type Ia supernovae (SNe Ia) breaks down in underluminous, 1991bg-like SNe Ia. This breakdown may be due to the choice of parameter used as a stand-in for the width of the SN Ia light curve. Using the colour stretch parameter sBV instead of older parameters resolves this issue. Here, I assemble a sample of 14 nearby 1991bg-like SNe Ia from the literature, all of which have independent host-galaxy distance moduli and little to no reddening. I use Gaussian process regression to fit the light curves of these SNe in U/u, B, V, g, R/r, I/i, and H, and measure their peak absolute magnitudes. I find statistically significant (>5σ confidence level in the optical and >4σ in the near-infrared) correlations between the peak absolute magnitudes of the 1991bg-like SNe Ia and their sBV values in the range 0.2 < sBV < 0.6. These correlations are broadly consistent with fits to sBV < 0.7 SNe Ia with preliminary B- and V-band peak absolute magnitudes from the Carnegie Supernova Project and significantly inconsistent with similar fits to normal and transitional SNe Ia (with 0.7 < sBV < 1.1). The underluminous width-luminosity relation shown here needs to be properly calibrated with a homogeneous sample of 1991bg-like SNe Ia, after which it could be used as a rung on a new cosmological distance ladder. With surface-brightness fluctuations (or another non-Cepheid method) used to calibrate distances to nearby 1991bg-like SNe Ia, such a ladder could produce an independent measurement of the Hubble-Lemaître Constant, H0.

Inversion of soil carbon, nitrogen, and phosphorus in the Yellow River Wetland of Shaanxi Province using field in situ hyperspectroscopy

Soil nitrogen and phosphorus are directly related to soil quality and vegetation growth and are, therefore, a common research topic in studies on global climate change, material cycling, and information exchange in terrestrial ecosystems. However, collecting soil hyperspectral data under in situ conditions and predicting soil properties, which can effectively save time, manpower, material resources, and financial costs, have been generally undervalued. Recent optimization techniques have, however, addressed several of the limitations previously restricting this technique. In this study, hyperspectral data were taken from surface soils under different vegetation types in the wetlands of the Shaanxi Yellow River Wetland Provincial Nature Reserve. Through in situ original and first-order differential transformation spectral data, three prediction models for soil carbon, nitrogen, and phosphorus contents were established: partial least squares (PLSR), random forest (RF), and Gaussian process regression (GPR). The R2 and RMSR of the constructed models were then compared to select the optimal model for evaluating soil content. The soil organic carbon, total nitrogen, and total phosphorus content models established based on the first-order differential had a higher accuracy when modeling and during model validation than those of other models. Moreover, the PLSR model based on the original spectrum and the Gaussian process regression model had a superior inversion performance. These results provide solid theoretical and technical support for developing the optimal model for the quantitative inversion of wetland surface soil carbon, nitrogen, and phosphorus based on in situ hyperspectral technology.

Fault-Tolerant Control for Aircraft with Structural Damage Using Sparse Online Gaussian Process Regression

AbstractThis paper presents the design of data-driven fault-tolerant control using sparse online Gaussian process regression (SOGPR) to stabilize an aircraft with left-wing damage. The structural damage causes changes in mass, moment of inertia, center of gravity, and aerodynamic coefficients. These parameter variations deteriorate the performance of model-based nonlinear control methods. Hence, Gaussian process-based nonlinear dynamic inversion (GP-NDI) is proposed to compensate for uncertainties in situations of structural damage. Unlike parametric adaptive control approaches, Gaussian process regression is a non-parametric method that does not need prior information about uncertainties. And the proposed method implements SOGPR to reduce computational time and memory by incrementally updating the mean and variance. To compensate for the error in the estimated uncertainty, a robust control input is designed. In addition, a weighted delete score is used to improve the transient response. Numerical simulation results are compared with model reference adaptive control (MRAC) and nonlinear disturbance observer (NDO) to analyze a stabilizing and tracking performance in a structural damage situation.

Forecasting SARS-CoV-2 spike protein evolution from small data by deep learning and regression

The emergence of SARS-CoV-2 variants during the COVID-19 pandemic caused frequent global outbreaks that confounded public health efforts across many jurisdictions, highlighting the need for better understanding and prediction of viral evolution. Predictive models have been shown to support disease prevention efforts, such as with the seasonal influenza vaccine, but they require abundant data. For emerging viruses of concern, such models should ideally function with relatively sparse data typically encountered at the early stages of a viral outbreak. Conventional discrete approaches have proven difficult to develop due to the spurious and reversible nature of amino acid mutations and the overwhelming number of possible protein sequences adding computational complexity. We hypothesized that these challenges could be addressed by encoding discrete protein sequences into continuous numbers, effectively reducing the data size while enhancing the resolution of evolutionarily relevant differences. To this end, we developed a viral protein evolution prediction model (VPRE), which reduces amino acid sequences into continuous numbers by using an artificial neural network called a variational autoencoder (VAE) and models their most statistically likely evolutionary trajectories over time using Gaussian process (GP) regression. To demonstrate VPRE, we used a small amount of early SARS-CoV-2 spike protein sequences. We show that the VAE can be trained on a synthetic dataset based on this data. To recapitulate evolution along a phylogenetic path, we used only 104 spike protein sequences and trained the GP regression with the numerical variables to project evolution up to 5 months into the future. Our predictions contained novel variants and the most frequent prediction mapped primarily to a sequence that differed by only a single amino acid from the most reported spike protein within the prediction timeframe. Novel variants in the spike receptor binding domain (RBD) were capable of binding human angiotensin-converting enzyme 2 (ACE2) in silico, with comparable or better binding than previously resolved RBD-ACE2 complexes. Together, these results indicate the utility and tractability of combining deep learning and regression to model viral protein evolution with relatively sparse datasets, toward developing more effective medical interventions.

An active machine learning approach for optimal design of magnesium alloys using Bayesian optimisation

In the pursuit of magnesium (Mg) alloys with targeted mechanical properties, a multi-objective Bayesian optimisation workflow is presented to enable optimal Mg-alloy design. A probabilistic Gaussian process regressor model was trained through an active learning loop, while balancing the exploration and exploitation trade-off via an acquisition function of the upper confidence bound. New candidate alloys suggested by the optimiser within each iteration were appended to the training data, and the performance of this sequential strategy was validated via a regret analysis. Using the proposed approach, the dependency of the prediction error on the training data was overcome by considering both the predictions and their associated uncertainties. The method developed here, has been packaged into a web tool with a graphical user-interactive interface (GUI) that allows the proposed optimal Mg-alloy design strategy to be deployed.

3D Radiation Mapping Using Gaussian Process Regression with Intensity Projection

This article presents a novel approach for generating a three‐dimensional radiation map using data collected by mobile robots, aimed at monitoring radiation distribution in environments such as nuclear power plants. The proposed approach leverages Gaussian process regression with a novel adaptation of the inverse square law as a kernel function, which accurately reflects the physical characteristics of radiation, enabling precise mapping from uncertain data. Additionally, a method is proposed for constructing a comprehensive radiation map in 3D environments by estimating the radiation source and project the radiation data from sparse data. The effectiveness of the methodology is validated through simulations and experiments. Utilizing Octomap, a 3D spatial mapping tool, the study not only successfully visualizes radiation distribution in complex settings with multiple sources but also quantitatively demonstrates the enhanced accuracy of our approach compared to other existing methods. This research offers contributions in managing radiation risks, providing essential insights into the field.

Machine learning predictions for carbon monoxide levels in urban environments

The increasing carbon emissions in Malaysia necessitate accurate methods to track and control pollution levels. This study focuses on predicting carbon monoxide (CO) concentrations in Petaling Jaya using various machine learning models, and two important parameters, CO concentration and time, were considered in the analysis. Six distinct machine learning models were assessed to gauge their predictive capabilities. These models encompassed a range of regression modeling techniques namely; Linear, Tree, Gaussian Process, Ensemble of Trees, Support Vector, and Artificial Neural Networks (ANN) modelling. The Matern 5/2 Gaussian Process Regression (GPR) model consistently outperformed other models across all scenarios, demonstrating high R2 values and low RMSE, MSE, and MAE values. Specifically, in scenarios 1, 2, 3, and 4, the Matern 5/2 model exhibited the lowest RMSE (0.084–0.088) and highest R2 (0.97), highlighting its reliability and robustness in predicting CO concentrations. Additionally, the Rational Quadratic model achieved an R2 of 0.97 with an RMSE of 0.088 in scenario 1, while the Quadratic SVM excelled in scenario 3 with an R2 of 0.965 and low RMSE, MSE, and MAE values (0.085, 0.007, and 0.066). These findings provide valuable insights for environmental protection, renewable energy transition, energy efficiency, sustainable land use planning, and public awareness. However, acknowledging the study's single-area focus and potential limitations in representing diverse regions, further research is warranted to explore carbon emissions across varied areas and enhance the generalizability of the findings.

A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

Precise characterisation of HD 15337 with CHEOPS: A laboratory for planet formation and evolution

The HD 15337 (TIC 120896927, TOI-402) system was observed by the Transiting Exoplanet Survey Satellite (TESS), revealing the presence of two short-period planets situated on opposite sides of the radius gap. This offers an excellent opportunity to study theories of formation and evolution, as well as to investigate internal composition and atmospheric evaporation. We aim to constrain the internal structure and composition of two short-period planets situated on opposite sides of the radius valley:\ HD 15337 b and c. We use new transit photometry and radial velocity data. We acquired 6 new transit visits with the CHaracterising ExOPlanet Satellite (CHEOPS) and 32 new radial velocity measurements from the High Accuracy Radial Velocity Planet Searcher (HARPS) to improve the accuracy of the mass and radius estimates for both planets. We re-analysed the light curves from TESS sectors 3 and 4 and analysed new data from sector 30, correcting for long-term stellar activity. Subsequently, we performed a joint fit of the TESS and CHEOPS light curves, along with all available RV data from HARPS and the Planet Finder Spectrograph (PFS). Our model fit the planetary signals, stellar activity signal, and instrumental decorrelation model for the CHEOPS data simultaneously. The stellar activity was modelled using a Gaussian-process regression on both the RV and activity indicators. Finally, we employed a Bayesian retrieval code to determine the internal composition and structure of the planets. We derived updated and highly precise parameters for the HD 15337 system. Our improved precision on the planetary parameters makes HD 15337 b one of the most precisely characterised rocky exoplanets, with radius and mass measurements achieving a precision better than 2<!PCT!> and 7<!PCT!>, respectively. We were able to improve the precision of the radius measurement of HD 15337 c to 3<!PCT!>. Our results imply that the composition of HD 15337 b is predominantly rocky, while HD 15337 c exhibits a gas envelope with a mass of at least $0.01\ M_ oplus$. Our results lay the groundwork for future studies, which can further unravel the atmospheric evolution of these exoplanets and offer new insights into their composition and formation history as well as the causes behind the radius gap.

Machine-Learned Potential Energy Surfaces for Free Sodium Clusters with Density Functional Accuracy: Applications to Melting

Gaussian Process Regression based Gaussian Approximation Potential has been used to develop machine learned interatomic potentials having density functional accuracy, for free sodium clusters. The training data was generated from a large sample of over 100,000 data points computed for clusters in the size range of N = 40–200, where N denotes the number of atoms in the cluster, using the density functional method as implemented in the VASP code. Two models have been developed, model M1 using data for N = 55 only, and model M2 using additional data from larger clusters. The models are intended for computing thermodynamic properties using molecular dynamics. Hence, particular attention has been paid to improve the fitting of the forces. Although it was possible to obtain a good fit using the data of Na55 only, additional data points from larger clusters were needed to get better accuracies in energies and forces for larger sizes. Surprisingly, the model M1 could be significantly improved by adding about 50 data points per cluster from the larger sizes. Thus, it turns out that the best fit can be obtained by carefully selecting a small number of data points viz. 1,900 and 1,300 configurations for the two models M1 and M2, respectively. These two models have been deployed to compute the heat capacities of Na55. The heat capacities of Na147 and about 40 isomers for larger clusters of sizes N = 147, 200, 201, and 252, have been obtained using the final model M2. There is an excellent agreement between the computed and experimentally measured melting temperatures. The geometries of these isomers have been further optimized by density functional theory. The mean absolute error with respect to DFT energies is found to be about 7 meV/atom or less. The errors in the lowest interatomic bond lengths are below 2% in almost all the cases.

Machine Learning-Assisted design of boron and nitrogen doped graphene nanosheets with tailored thermomechanical properties

Doping graphene with boron and/or nitrogen enhances its potential for various applications, such as electronics and energy devices. However, these modifications impact the material's properties, influencing its response to external forces, temperature, and heating. Investigating the connection between the structure of co-doped graphene nanosheets and their thermomechanical properties is crucial for accurate predictions and tailored nanosheet engineering. In the present study, molecular dynamics (MD) simulations were performed to compute the thermal and mechanical properties of 300 randomly generated boron/nitrogen co-doped graphene nanosheets with doping concentrations in the range of 0%-15%. Next, the obtained MD results were used to train, tune, and validate a wide spectrum of supervised machine learning models, including linear regression models, regression trees, support vector machines, Gaussian process regression models, kernel approximation models, ensembles of regression trees, and regression neural networks. Our aim is to find models that better estimate, without overfitting, the structure-properties relation of boron/nitrogen co-doped nanosheets. To this end, the models with the highest coefficient of determination (R2) and the lowest root mean square error (RMSE) were utilized. Finally, an appropriate implementation of guided random search algorithms, mainly Genetic Algorithms, was used to solve the inverse problem, i.e., find the nanosheet structure which exhibits the desired set of property values. To this end, thermal conductivity, Young’s modulus, failure stress, and failure strain were specified as target values. A detailed comparison between the employed models and their validation via MD simulations is also included. The achieved results provide sufficient evidence of the accuracy and viability of the applied procedure in both prediction of thermomechanical properties as well as identification of structures with desired properties. This study provides a roadmap that could help scientists and engineers develop nanosheets-based materials with tunable thermomechanical properties, ultimately leading to the creation of innovative and high-performance technologies.

Fast-running CFD calculations of the ONR Tumblehome performing maneuvers in calm water and in waves using a Gaussian process regression propeller and rudder model

The accurate and efficient prediction of vessel maneuvering characteristics in calm water and in waves using numerical methods is challenging. The objective of this work is to demonstrate the use of a Gaussian Process Regression based data-driven propeller and rudder model for vessel maneuvering in both calm water and in waves. The data-driven propeller and rudder model is trained with CFD simulations of the discretized propeller and rudder operating in the behind condition at different forward speeds, drift angles, and rudder angles. The data-driven propeller and rudder model enables the accurate calculation of maneuvering performance with low computational expense. This work describes the process for training and implementing the data-driven propeller and rudder model in a CFD package. The calm water zigzag and turning circle maneuvering characteristics for the ONR Tumblehome are evaluated and are compared to archival experiments. Furthermore, the maneuvering characteristics are evaluated in regular waves with several different wave conditions. In addition to demonstrating the accurate and efficient calculation of maneuvering performance, this work provides a multi-fidelity database of propeller and rudder forces at different forward speeds and drift angles, which can be used to train future data-driven propeller and rudder models.

Integrating UAV hyperspectral data and radiative transfer model simulation to quantitatively estimate maize leaf and canopy nitrogen content

Crop nitrogen (N) content reflects crop nutrient status and plays an important role in precision nutrient management. Accurate crop N content estimation from remote sensing has been well documented. However, the robustness (i.e., the ability of a model to perform consistently across various conditions) of these methods under varied soil conditions or different growth stages has rarely been considered. We proposed a hybrid method that integrates in-situ measurements and the data simulated by a mechanistic model to improve the estimation of maize N content. In-situ data included hyperspectral images collected by Unmanned Aerial Vehicle (UAV), and leaf and canopy N content (LNC and CNC). A mechanistic radiative transfer model (PROSAIL-PRO) was used to generate simulated data, i.e., canopy reflectance paired with target crop traits (i.e., LNC, CNC). We compared the performance from the hybrid method with a machine learning method (Gaussian Process Regression) and six different vegetation indices (VIs) on four in-situ datasets collected at three study sites from 2021 to 2022. Results show that the hybrid method consistently performed the best for LNC estimation across four testing datasets (RRMSE ranging from 10.08% to 10.84%). For CNC estimation, the hybrid method had the best estimation results on two out of the four testing datasets and performed comparably to the best method on the other two datasets (RRMSE ranging from 13.89% to 25.21%). Next, we assessed the estimation robustness of the hybrid method, the machine learning, and the best-VI by comparing the mean (µ) and standard deviation (σ) of RRMSE across diverse water and N treatments (condition #1) and different growth stages (condition #2). Among 16 total cases (two crop traits by four study sites by two conditions), the hybrid method had 11 cases of smallest µ and seven cases of smallest σ, outperforming the machine learning (0/16 for µ, 4/16 for σ) and the best-VI (5/16 for µ, 5/16 for σ). These results underscore the greater robustness of the hybrid method. This study highlights the potential of integrating in-situ measurements and simulated data to improve estimation accuracy and robustness for maize LNC and CNC. The promising performance of the hybrid method suggests its applicability to a broader range of crops and various crop traits.